Live Exercise 3: Optimal Patent Length — the Ideas Model

MSc-level Industrial Organisation course at the University of St Andrews
Author

Gerhard Riener

Group exercise (≈20 minutes)

Problem: Patent length and the ideas model

A patent regulator is evaluating two candidate drugs under the Scotchmer ideas model. Each drug is characterised by a pair \((\nu, F)\), where \(\nu\) is the per-period consumer surplus under competitive supply and \(F\) is the fixed development cost.

The regulatory parameters are:

\[ \pi = \tfrac{1}{2}, \qquad \lambda = \tfrac{1}{4}, \qquad r = \tfrac{1}{4}, \]

where \(\pi\) is the share of per-period consumer surplus appropriated by the patent holder as profit, \(\lambda\) is the per-period deadweight loss as a share of \(\nu\), and \(r\) is the discount rate. The current (discounted) patent length is \(T = 20\).

Drug \(\nu\) \(F\)
Alpha 10 60
Beta 5 10

(a) Private investment condition

For each drug, determine whether a firm will voluntarily invest given \(T = 20\).

The investment condition is: \(\pi \nu T \ge F\).

(b) Net social value

For each drug, compute the net discounted social value of development:

\[ \text{Social value} = \frac{\nu}{r} - \lambda \nu T - F. \]

(Note: with \(r = \tfrac{1}{4}\), the perpetual benefit per unit of \(\nu\) is \(\tfrac{1}{r} = 4\).)

Does either drug yield a positive net social surplus at \(T = 20\)?

(c) Socially optimal patent length for Drug Beta

Find the minimum patent length \(T^*\) that just induces private investment in Drug Beta. At \(T = T^*\), compute the net social value and state your conclusion.

(d) Discussion (5 minutes)

At \(T = 20\), both drugs are privately profitable yet socially wasteful. Drug Beta becomes socially efficient at a much shorter patent length.

  1. What does this imply for the design of a uniform patent length (the same \(T\) for all drugs)?
  2. Why is it difficult in practice to implement drug-specific patent lengths, even if they would be welfare-improving?